Convergence Analysis for Particle Swarm Optimization
Particle swarm optimization (PSO) is a very popular, randomized, nature-inspired meta-heuristic for solving continuous black box optimization problems. The main idea is to mimic the behavior of natural swarms like, e. g., bird flocks and fish swarms that find pleasant regions by sharing information....
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| Taal: | Engels |
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FAU University Press
2025
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| Online toegang: | ONIX_20250828T094736_9783944057309_19 |
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| _version_ | 1869527832008327168 |
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| author | Schmitt, Berthold Immanuel |
| author_browse | Schmitt, Berthold Immanuel |
| author_facet | Schmitt, Berthold Immanuel |
| author_sort | Schmitt, Berthold Immanuel |
| collection | Directory of Open Access Books |
| description | Particle swarm optimization (PSO) is a very popular, randomized, nature-inspired meta-heuristic for solving continuous black box optimization problems. The main idea is to mimic the behavior of natural swarms like, e. g., bird flocks and fish swarms that find pleasant regions by sharing information. The movement of a particle is influenced not only by its own experience, but also by the experiences of its swarm members. In this thesis, we study the convergence process in detail. In order to measure how far the swarm at a certain time is already converged, we define and analyze the potential of a particle swarm. This potential analysis leads to the proof that in a 1-dimensional situation, the swarm with probability 1 converges towards a local optimum for a comparatively wide range of objective functions. Additionally, we apply drift theory in order to prove that for unimodal objective functions the result of the PSO algorithm agrees with the actual optimum in k digits after time O(k). In the general D-dimensional case, it turns out that the swarm might not converge towards a local optimum. Instead, it gets stuck in a situation where some dimensions have a potential that is orders of magnitude smaller than others. Such dimensions with a too small potential lose their influence on the behavior of the algorithm, and therefore the respective entries are not optimized. In the end, the swarm stagnates, i. e., it converges towards a point in the search space that is not even a local optimum. In order to solve this issue, we propose a slightly modified PSO that again guarantees convergence towards a local optimum. |
| format | Online |
| id | doab-20.500.12854ir-166254 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | FAU University Press |
| publisherStr | FAU University Press |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1662542025-10-16T12:46:55Z Convergence Analysis for Particle Swarm Optimization Schmitt, Berthold Immanuel Laufzeitanalyse Partikel-Schwarm-Optimierung Drifttheorie thema EDItEUR::U Computing and Information Technology thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes Particle swarm optimization (PSO) is a very popular, randomized, nature-inspired meta-heuristic for solving continuous black box optimization problems. The main idea is to mimic the behavior of natural swarms like, e. g., bird flocks and fish swarms that find pleasant regions by sharing information. The movement of a particle is influenced not only by its own experience, but also by the experiences of its swarm members. In this thesis, we study the convergence process in detail. In order to measure how far the swarm at a certain time is already converged, we define and analyze the potential of a particle swarm. This potential analysis leads to the proof that in a 1-dimensional situation, the swarm with probability 1 converges towards a local optimum for a comparatively wide range of objective functions. Additionally, we apply drift theory in order to prove that for unimodal objective functions the result of the PSO algorithm agrees with the actual optimum in k digits after time O(k). In the general D-dimensional case, it turns out that the swarm might not converge towards a local optimum. Instead, it gets stuck in a situation where some dimensions have a potential that is orders of magnitude smaller than others. Such dimensions with a too small potential lose their influence on the behavior of the algorithm, and therefore the respective entries are not optimized. In the end, the swarm stagnates, i. e., it converges towards a point in the search space that is not even a local optimum. In order to solve this issue, we propose a slightly modified PSO that again guarantees convergence towards a local optimum. 2025-08-29T05:06:09Z 2025-08-29T05:06:09Z 2025-08-28T07:59:02Z 2015 book ONIX_20250828T094736_9783944057309_19 https://library.oapen.org/handle/20.500.12657/105775 9783944057309 https://directory.doabooks.org/handle/20.500.12854/166254 eng FAU Forschungen : Reihe B open access image/jpeg image/jpeg n/a n/a https://library.oapen.org/bitstream/20.500.12657/105775/1/9783944057309.pdf https://library.oapen.org/bitstream/20.500.12657/105775/1/9783944057309.pdf FAU University Press 2c600dea-eece-4066-87be-da335e323fdb 9783944057309 AG Universitätsverlage 214 Erlangen open access |
| spellingShingle | Laufzeitanalyse Partikel-Schwarm-Optimierung Drifttheorie thema EDItEUR::U Computing and Information Technology thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes Schmitt, Berthold Immanuel Convergence Analysis for Particle Swarm Optimization |
| title | Convergence Analysis for Particle Swarm Optimization |
| title_full | Convergence Analysis for Particle Swarm Optimization |
| title_fullStr | Convergence Analysis for Particle Swarm Optimization |
| title_full_unstemmed | Convergence Analysis for Particle Swarm Optimization |
| title_short | Convergence Analysis for Particle Swarm Optimization |
| title_sort | convergence analysis for particle swarm optimization |
| topic | Laufzeitanalyse Partikel-Schwarm-Optimierung Drifttheorie thema EDItEUR::U Computing and Information Technology thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes |
| topic_facet | Laufzeitanalyse Partikel-Schwarm-Optimierung Drifttheorie thema EDItEUR::U Computing and Information Technology thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes |
| url | ONIX_20250828T094736_9783944057309_19 |
| work_keys_str_mv | AT schmittbertholdimmanuel convergenceanalysisforparticleswarmoptimization |